Comparative analysis of rigidity across protein families

Abstract

Is the rigidity transition in proteins similar to that of glassy networks? This is a comparative study in which the ‘pebble game’ rigidity analysis software FIRST is used to study multiple protein crystal structures, from six different protein families. We chose crystal structures from the Protein Data Bank at resolution <2.5A that represent homologous proteins from different organisms, or the same protein crystalised under different conditions. Rigidity analysis is performed by removing hydrogen bonds in order, from weakest to strongest, and balancing the protein structure constraints against the atomic degrees of freedom. This gives a rigidity-flexibility measure, which we use to compare the rigidity dilution of the different sets of proteins. We find that the main-chain rigidity of a protein structure at a given hydrogen bond energy cutoff is quite sensitive to small structural variations, and conclude that the hydrogen bona constraints in rigidity analysis should be chosen so as to form and test specific hypotheses about the rigidity of a particular protein. Our comparative approach highlights two different characteristic patterns (‘sudden’ or ‘gradual’^ for protein rigidity loss as constraints are removed, in line with recent results on tne rigidity transitions of glassy networks. Our study highlights the fact that proteins rigidity dilution can show first or second order behaviour, as in glassy networks, and that the choice of the energy cutoff used for further explorations of protein properties needs to be chosen taking into account each protein’s particular rigidity dilution.